Explain why f must be a di?erentiable function, Mathematics

Assignment Help:

Let f : R3 → R be de?ned by:
                                       f(x, y, z) = xy2+ x3z4+ y5z6

a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) .

b) Brie?y explain why f must be a di?erentiable function (you just need to "look" at the equations for the partial derivatives).

c) Find D~uf(2, 1, 1) where ~u is a unit vector in the direction of ~v = h4, 3,-1i .

d) Find an equation for the plane which is tangent to the surface de?ned by

xy2+ x3z4+ y5z6= 11

 at the point (2, 1, 1) .

e) Use di?erentials to approximate the value of f(2.01, 1.02, 0.97) . Use a calculator to
?nd a more accurate value, and compare.


Related Discussions:- Explain why f must be a di?erentiable function

How many people said that red was their favorite color, In a recent survey ...

In a recent survey of 700 people, 15% said that red was their favorite color. How many people said that red was their favorite color? Find out 15% of 700 through multiplying 70

Space geometry, a sketch of two dimensional system

a sketch of two dimensional system

#tnumarancyitle.., what is classification and how can you teach it?

what is classification and how can you teach it?

Dora, dora and her family are driving to visit relatives for the holidays t...

dora and her family are driving to visit relatives for the holidays they travel 174 miles in 3 hours if they travel at a constant speed how many miles do they travel in one hourest

Ratio, There are only Chinese and Malay pupils in a hall.The ratio of the n...

There are only Chinese and Malay pupils in a hall.The ratio of the number of boys to the number of girls is 2:3.The ratio of the number of Chinese boys to the number of Malay boys

Comperative statics, Discuss comparative statics,Market model and Nationa i...

Discuss comparative statics,Market model and Nationa income model

Determine the number of full withdrawals, A worker retires with a lump sum ...

A worker retires with a lump sum superannuation benefit of $500,000. She immediately invests this money in a fund earning 5% pa effective. One year after retirement she begins maki

Define histogram, Q. Define histogram? Ans. A histogram is a bar g...

Q. Define histogram? Ans. A histogram is a bar graph that gives the frequency of each value. Here are a few examples to illustrate the usefulness of this method of data r

Method of reduction of order, Consider the equation x 2 y′′+ xy′- y = 4x...

Consider the equation x 2 y′′+ xy′- y = 4x ln x (a) Verify that x is a solution to the homogeneous equation. (b) Use the method of reduction of order to derive the second

Evaluate the slope of the line, Evaluate the slope of the line: Examp...

Evaluate the slope of the line: Example: What is the slope of the line passing through the points (20, 85) and (30, 125)? Solution:            m = 125 -85/30-20 = 4

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd